About

Incorrect allele frequency estimation propagates errors into linkage disequilibrium analysis, association studies, and forensic match probability calculations. A miscounted genotype class or a rounding shortcut can shift p by enough to invert a chi-square verdict on Hardy-Weinberg equilibrium. This calculator applies the direct counting method - p = (2 × N_AA + N_Aa) ÷ 2N - and returns expected genotype counts under HWE (p², 2pq, q²), a Pearson chi-square goodness-of-fit statistic with associated p-value, observed and expected heterozygosity, and Wright's fixation index F. It supports two-allele and three-allele loci. Results assume a diploid, randomly mating population with no selection, migration, mutation, or drift. Small sample sizes (N < 30) yield unreliable chi-square approximations; exact tests are preferable in that range.

Formulas

The core relationship governing a randomly mating diploid population at a bi-allelic locus:

p² + 2pq + q² = 1

where p + q = 1. Allele frequencies from observed genotype counts:

p = 2N_AA + N_Aa2N

Expected genotype counts under Hardy-Weinberg equilibrium:

E_AA = p² × N , E_Aa = 2pq × N , E_aa = q² × N

Chi-square goodness-of-fit test:

χ² = k∑i=1 (O_i − E_i)²E_i

Expected heterozygosity and fixation index:

H_e = 1 − k∑i=1 p_i² , F = H_e − H_oH_e

For a three-allele system (p + q + r = 1), six genotype classes exist: p², q², r², 2pq, 2pr, 2qr. The chi-square test uses df = 3 (6 genotype classes minus 3 allele frequency parameters).

Where: p, q, r = allele frequencies; N = total individuals; O_i = observed count for genotype i; E_i = expected count; H_e = expected heterozygosity; H_o = observed heterozygosity; F = Wright's fixation index (positive = heterozygote deficit, negative = excess).

Reference Data

Parameter	Symbol	Formula / Definition	Typical Range
Dominant allele frequency	p	(2N_AA + N_Aa) ÷ 2N	0 - 1
Recessive allele frequency	q	1 − p	0 - 1
Expected AA frequency	p²	Homozygous dominant	0 - 1
Expected Aa frequency	2pq	Heterozygote	0 - 0.5
Expected aa frequency	q²	Homozygous recessive	0 - 1
Chi-square statistic	χ²	∑((O − E)² ÷ E)	0 - ∞
Degrees of freedom (2-allele)	df	Genotypes − alleles	1
Degrees of freedom (3-allele)	df	6 − 3 = 3	3
Expected heterozygosity	H_e	1 − ∑p_i²	0 - 1
Observed heterozygosity	H_o	Heterozygotes ÷ N	0 - 1
Fixation index	F	(H_e − H_o) ÷ H_e	−1 to 1
HWE significance (α)	α	Conventional threshold	0.05
Carrier frequency (2-allele)	2pq	Proportion carrying one recessive allele	0 - 0.5
Cystic fibrosis (q)	-	European Caucasians	0.022
Sickle cell (q)	-	West African populations	0.10 - 0.20
PKU (q)	-	European Caucasians	0.010
Tay-Sachs (q)	-	Ashkenazi Jewish	0.018
CCR5-Δ32 (q)	-	Northern European	0.10
ABO locus alleles	p, q, r	I^A, I^B, i frequencies	Varies by population
MN blood group	-	Co-dominant, classic HWE example	p ≈ 0.54

Frequently Asked Questions

A positive F signals a deficit of heterozygotes relative to Hardy-Weinberg expectation. Common causes include inbreeding (consanguineous mating), population substructure (Wahlund effect), or positive assortative mating. An F of 0.05 is often considered a threshold for mild inbreeding in human populations. Values approaching 1.0 indicate near-complete homozygosity.

The chi-square statistic scales linearly with sample size N. A genotype frequency that deviates from expectation by 0.5% may be statistically significant at N > 10000 even though the biological significance is negligible. Always report effect size (the fixation index F) alongside the p-value. Statistical significance is not biological significance.

Null alleles produce no detectable product (e.g., failed PCR amplification at a microsatellite locus). Null/null homozygotes appear as missing data, and null/visible heterozygotes are misclassified as visible homozygotes. This inflates observed homozygosity, biases F upward, and makes the population appear to violate HWE. Software such as Micro-Checker or ML-NullFreq can estimate null allele frequency. If null allele frequency exceeds 0.05, consider dropping the locus.

No. This tool assumes autosomal diploid loci. For X-linked loci, males are hemizygous and genotype expectations differ by sex: females follow standard HWE (p², 2pq, q²) while males have frequencies p and q directly. Pooling sexes without correction produces spurious HWE deviations.

The chi-square approximation requires all expected cell counts E_i ≥ 5. For a rare allele with q = 0.05, the expected homozygote count is q² × N = 0.0025N, so you need N ≥ 2000 for that cell alone. Below this threshold, use an exact test (Fisher or permutation). This calculator flags when any expected count falls below 5.

HWE assumes no fitness differences among genotypes. If heterozygotes have higher fitness (heterozygote advantage, as with sickle cell trait in malaria-endemic regions), the population will maintain higher heterozygosity than HWE predicts, producing a negative F. Directional selection against homozygous recessives reduces q slowly because most recessive alleles hide in heterozygous carriers. The rate of change in q per generation under complete selection against aa is Δq = −q²1 + q.